All perfect praise be to Allah, The Lord of The Worlds, and may His peace and blessings be upon our Prophet Muhammad and upon all of his family and companions.

The Sharia ruling in this regard is based on the medical doctors' consultation as well their explanation regarding the aforementioned delivery as precisely as possible:

If they determined that the most probable cause of death was the malpractice delivery, then the midwife mentioned above is liable and obliged to pay Diya to the heirs of the baby as well to fast for two consecutive months for the Prophet (PBUH) said (What means):" the Messenger of Allah said: "Whoever practices medicine when he is not known for that, he is liable." [Related by Abu Dawood].

In this regard, Al-Khatabee (May Allah have mercy on his soul) stated:" If a doctor negligence caused an injury or damage to one of the patient's organs, then he is responsible for that. And whosoever practice a science or job in which he is unacquainted such as medicine and cause damage or injury to the patient due to his practice, then he is obliged to pay Diya and there is no need for the implementation of the prescribed punishments, because treatment won't be applied without the patient's full consent; finally, the blood relatives of the doctor are obliged to help in paying Diya according the majority of Muslim jurists in case of damage or injury inflicted over his patient." [Ma'alim Al-Sunn vol. 4/ pp. 39].

In addition, Al-Imam Ashafiee' (May Allah be pleased with him) stated:" If a person was asked to apply cupping, circumcising a child or treating an animal and damage incurred while he is fully acquainted with all of  above procedures according to specialists in this regard, then he won't be liable at all; but if he conducted the above procedures without having any knowledge and was aware of it, then he is responsible for all of his actions." [Al-Oom vol.6 pp. 185].

Yet, if doctors determined that the cause of your baby's (Questioner) death was normal due to the delay of treatment, or they were suspicious and unable to determine the real cause of death, then she (Midwife) isn't liable for expiation nor Diya because in principle, she is free from the liability regarding the baby's condition save if doctors made sure that his death was due to her malpractice.

Finally, in all cases, the midwife should adhere to seeking  forgiveness from Allah and ask Him to pardon all of her actions in the past. Kindly refer to [Ahkam Al-Jiraha vol.519 pp. 534]. And Allah knows best.